>>Read it again. I didn't say it was impossible for a system to become more ordered. I DID say that it is impossible for the net Entropy change of the Universe to be negative. If the Entropy of the system becomes negative the Etropy of the surroundings becomes more postive, resulting in a net postivie Entropy change of the Universe. These statements are based on the three Laws of Thermodynamics, which has been under constant testing since they were first formulated by Carnot over two hundered years ago. The rules can be expressed simply: You can't get more out of a process than what you put in. You can't even get out of a process what you put in. You can't get out of the game. You can't get more work out of a gallon of gasoline than the equivilent calories in that gallon. You can't even get that much work out of a gallon of gasoline. You can't get to Absolute Zero Kelvin.
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>>>It's just like the lottery - the order of numbers selected appears random, but you have an equal probability of winning if you pick the numbers 1,2,3,4,5,6 every week as you do if you pick a random selection.
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>>No, it's not like the lottery. The Entropy change of the Universe cannot be randomly positive or negative. It is ALWAYS positive. This is how we separate possible things from impossible things, which is why you will never see a spilt cup of coffee come together on the floor at the point of impact and then recombine and fly back up to the table. Nor will you ever see a set of billiard balls reform themselves into an ordered triangle on the billiard table, without intervention. Even with intervention the Entropy increase of the intervener is greater than the Entropy loss the balls experience when they are reordered.
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>>I say it again: The only physical changes which can occur are those for which the Entropy of the Universe increases. Human intelligence has nothing to do with it and cannot change the outcome.
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>I don't agree completely here (only almost). As far as my studies on entropy go, they are indeed based on probability. With a small system (a few atoms), it is indeed possible for entropy to decrease - even without a larger system gaining entropy. With a larger system (e.g., the Universe), this is possible only in theory. The reason that the Second Law of Thermodynamics is found to be always true is that it deals with large groups of atoms. Any violation (like the broke cup of coffee rearranging itself) is possible in theory - however, it is so extremely unlikely (because a large amount of atoms have to work together, by pure chance), that for any practical purpose, the probability can be considered zero.
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>Hilmar.

You are refering to colligative properties, like radioactive decay. Properties of matter which manifest themselves only in a collection of objects. Themodynamics is not based on colligative properties. It is based on energy flows between one or particles. The probability view of Entropy states that S = k*ln(W), where W is the number of states, and is an analyis that doesn't use energy flow, and is not applicable in all cases because it is a colligative approach. Themodynamics at both the particle and the quantum level (which includes subatomic particles and gets below and around the colligative approach) follow precise mathematical principles. No handwaving is envolved. The dichotomy of the universe into the system under study and the environment (U = S + E) eliminates etherial entities.

The main reason why a violation of the three laws of thermo is not possible is because EVERY engine which extracts work has to operate between two temperatures. Heat cannot flow between two sources at the same temperature. In order to circumvent the 2nd Law one must violate the 3rd, or Zeroth law. Namely, the heat sink must be at or below Absolute Zero Kelvin. Below Zero Kelvin is not possible. So, that leaves only that an engine (or refridgerator) must dump a certain amount of heat into a sink which as a temperature of Zero Kelvin. If it could do that then it could operate at 100% efficency. That is, every calorie of heat taken from the high temperature souce would be converted into useful work, with NO heat being dumped to the Zero Kelvin sink. The Zeroeth Law says that reaching Zero Kelvin is impossible. Why? To do so would require an engine with a heat sink whose temperature is below Zero Kelvin. Negative Kevin temperatures don't exist because Zero Kelvin is defined as the temperature at which all motion, including atomic motion ceases. We have been able to get within a few millionths of a degree of Zero Kelvin, as defined by the temperature of the heat sink in the engine we have devised to do so.
JLK